2022-10-09

Making sense of this formula relating to polynomials :
$P\left(x+n+1\right)=\sum _{i=0}^{n}\left(-1{\right)}^{n-1}\left(\genfrac{}{}{0}{}{n+1}{i}\right)P\left(x+i\right)$

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lascosasdeali3v

Expert

"If you take the right side over to the left (correcting a minor typo - ""n-1"" should be ""n-i"" in the power of -1), the equation can also be written like this:

What this is, is actually the iterated difference. That is, if

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